分数傅里叶变换的快速算法及计算全息图的研究

通过分析菲涅耳衍射积分的快速算法，依据Lohmann提出的任意阶的分数傅里叶变换的单透镜光学实验装置，详细分析丁光场在此单透镜系统中的传播过程，提出了一种基于傅里叶变换的分数傅里叶变换快速算法，并对基于此快速算法的分数傅里叶变换全息图的计算机生成与数字重现进行了研究。实验结果示出了分数傅里叶变换全息图及其在重构过程中分数阶匹配与否的实验结果，验证了分数傅里叶变换分数阶的重要性质和笔者提出算法的可行性。     

连续子波变换的MATLAB实现分析

本文目的在于考察序列信号的连续子波变换（CWT）在MATLAB中的程序实现。首先介绍子波变换的基本概念和MATLAB中的算法原理，对MATLAB中的cwt．m程序进行深入解读，阐述了各个参数的功能；而后发现差分运算的存在使子波滤波器系数含有误差，继而对此误差的产生原因进行分析，解释如何调整cwt．m算法中的参数，以克服差分运算的影响，改善子波滤波器系数的取值，并且提出一种新算法，改善了CWT变换的运算效果；最后以频移键控FSK信号为例，分别用两种算法对之进行连续子波变换．并对结果进行分析和比较．证明了本文的改追算法优于MATLAB中的原算法。     

基于听觉模型的子波变换语音处理

首先讨论了人类听觉信号处理的原理，进而将基于听觉模型的子波变换（ＷＴ）与短时傅里叶变换（ＳＴＦＴ）进行了比较，突出了ＷＴ信号处理的独特之处。然后，简要讨论了其在语音处理中的应用。最后，给出了应用ＷＴ来进行声、韵母划分和音素周期检测的实验，其结果显示了ＷＴ在语音处理中的良好性能。     

傅氏去卷积和小波理论用于谱图分峰的对比研究

对小波理论和傅里叶变换去卷积数学方法在谱图分峰中的应用做了对比研究，对于完全重叠的谱峰用傅里叶变换去卷积方法效果较好，而对于不完全重叠的谱用小波方法处理效果较好。     

利用基本信号求解复杂信号的傅里叶变换

在信号与系统的教学过程中,求解信号的傅里叶变换一直是教学中的重点和难点,特别是对复杂信号傅里叶变换的求解,很多学生感到无从下手.介绍了一种在时域中将复杂信号用基本信号来表示,再通过基本信号的傅里叶变换,以及傅里叶变换的性质来求解复杂信号傅里叶变换的方法,有助于提高学生的学习兴趣,培养学生的工程思维能力,拓宽了解题思路.     

分数傅里叶变换的快速算法及计算全息图的研究

通过分析菲涅耳衍射积分的快速算法,依据Lohmann提出的任意阶的分数傅里叶变换的单透镜光学实验装置,详细分析了光场在此单透镜系统中的传播过程,提出了一种基于傅里叶变换的分数傅里叶变换快速算法,并对基于此快速算法的分数傅里叶变换全息图的计算机生成与数字重现进行了研究。实验结果示出了分数傅里叶变换全息图及其在重构过程中分数阶匹配与否的实验结果,验证了分数傅里叶变换分数阶的重要性质和笔者提出算法的可行性。     

大气探测傅里叶变换光谱仪

高精度的大气红外光谱遥感是实现数值天气预报、进行环境监测等应用的关键技术。论述了星载大气探测傅里叶变换光谱系统在完成这一高精度遥感测量中的重要地位及其发展与现状,从应用的角度提出了大气探测傅里叶变换光谱仪器光谱波段、分辨率等技术指标的要求,讨论了仪器的总体设计方案,提出了成功地进行大气傅里叶光谱探测所必须解决的关键技术。     

一种快速线性时频变换方法

信号的频率含量在很多应用中是非常重要的,很多算法在这方面进行了研究。普通的S变换可以同时提供时间和频率信息,但需要的计算要求较高。本文介绍了一种线性时频变换方法,包括傅里叶变换（FT）、短时傅里叶变换（STFT）和S变换（ST）。它是一种离散的,可逆的,无冗余的变换算法,具有快速傅里叶变换（FFT）相同的计算复杂度。经过合理的调试和仿真,该方法有效地对非平稳信号频谱进行采样和加窗过滤,得到连续S变换频谱,说明在信号分析中具有可行性和适用性。     

科氏质量流量计应用技术探讨

介绍了科里奥利(Coriolis)质量流量计(以下简称CMF)测量流体质量流量的幅值比测量法、时间差的直接测量法及傅里叶变换算法的测量原理,同时还介绍了相关技术及锁相环技术在测量中的应用。文中给出了对太航某型号CMF的传感器在不同流量情况下进行A/D同步采样后,应用锁相环技术和傅里叶变换算法,用MATLAB软件得到不同流量对应的相位差曲线图。最后对以上三种算法进行了比较分析。结果表明,傅里叶变换算法的应用是模拟式CMF转化到数字式CMF的关键因素,并且可以有效提高计量精度。     

FT、ZT、DFS、DFT和FFT变换的特点及相互关系

针对信号处理中常用的傅里叶变换FT、Z变换、离散傅里叶级数DFS、离散傅里叶变换DFT和快速傅里叶变换FFT等几种重要的变换,从它们的定义、时频域表达式、物理意义和图形等方面进行分析,归纳总结出这几种变换的特点及它们之间的关系。     

Beta wavelets. Synthesis and application to lossy image compression

Wavelets are known to have many connections to several other parts of mathematics, notably phase-space analysis of signal processing, reproducing kernel Hilbert spaces, coherent states in quantum mechanics, spline approximation theory, windowed Fourier transforms, filter banks and image analysis.In this paper, we study a new orthogonal mother wavelet and wavelet basis system based on Beta function as well as its derivatives. The most important conditions of mother wavelets to be satisfied are the admissibility, the regularity and the orthogonality. All these conditions were verified in the case of the proposed Beta wavelets family.Compared to most known wavelets as Haar, Daubechies, and Coifflet ones, the Beta wavelet family improves efficient results and performances presented in this paper for image compression context.     

Curvature analysis of frequency modulated manifolds in dimensionality reduction

Recent advances in the analysis of high-dimensional signal data have triggered an increasing interest in geometry-based methods for nonlinear dimensionality reduction (NDR). In many applications, high-dimensional datasets typically contain redundant information, and NDR methods are important for an efficient analysis of their properties. During the last few years, concepts from differential geometry were used to create a new range of NDR methods. In the construction of such geometry-based strategies, a natural question is to understand their interaction with classical and modern signal processing tools (convolution transforms, Fourier analysis, wavelet functions). In particular, an important task is the analysis of the incurred geometrical deformation when applying signal transforms to the elements of a dataset. In this paper, we propose the concepts of modulation maps and modulation manifolds for the construction of particular datasets relevant in signal processing and NDR. We consider numerical methods for analyzing geometrical properties of the modulation manifolds, with a particular focus on their scalar and mean curvature. In our numerical examples, we apply the resulting geometry-based analysis to simple test cases, where we present geometrical and topological effects of relevance in manifold learning.     

多传感器单模型动态系统多尺度分布式融合估计

近几年来,小波理论和信号的多尺度表示方法都得到了迅速发展,并在包括信号处理和图像处理在内的众多领域中得到了成功的应用,而在这些领域中,目前一个较为活跃的分支是基于小波变换的多尺度表示的统计信号处理。运用多尺度分析的思想,将基于模型的动态系统分析方法与基于统计特性的多尺度信号变换方法相结合,建立起状态基于多源观测信息的多尺度分布式融合估计和单源观测信息的多尺度分布式估计两种新算法,用计算机仿真研究验证了算法效能。     

Three-dimensional quantum wavelet transforms

Wavelet transform is being widely used in the field of information processing. One-dimension and two-dimension quantum wavelet transforms have been investigated as important tool algorithms. However, three-dimensional quantum wavelet transforms have not been reported. This paper proposes a multi-level three-dimensional quantum wavelet transform theory to implement the wavelet transform for quantum videos. Then, we construct the iterative formulas for the multi-level three-dimensional Haar and Daubechies D4 quantum wavelet transforms, respectively. Next, we design quantum circuits of the two wavelet transforms using iterative methods. Complexity analysis shows that the proposed wavelet transforms offer exponential speed-up over their classical counterparts. Finally, the proposed quantum wavelet transforms are selected to realize quantum video compression as a primary application. Simulation results reveal that the proposed wavelet transforms have better compression performance for quantum videos than two-dimension quantum wavelet transforms.     

Vibration modelling with fast Gaussian wavelet algorithm

Vibration signals are considered as nonstationary signals with transients. Conventional harmonic Fourier analysis finds it difficult to model the vibration signals. In this paper, a novel approach using the global Fourier transforms and local wavelet analysis is presented for vibration analysis and modelling. Time–frequency wavelet analysis has been proven a useful tool for the detection of vibration transients. However, current algorithms with discrete or continuous wavelet transforms for vibration analysis are either low resolution of features or very time consuming. We developed a fast Gaussian wavelet algorithm with very narrow band-pass filtering technique. The time–frequency maps with high frequency resolution enable us to observe the evolution in time of significant frequencies identified by global Fourier analysis, so that the transients and the regular signals can be distinguished. These regular significant frequencies are selected to be the basis of vibration modelling. The coefficients of the model are identified by a least-squares algorithm, which ensures that the error is minimised. To demonstrate this approach a machine spindle vibration signal is analysed, and the main features of the vibration signal are extracted, which are useful for system monitoring and further analysis.     

量子小波变换算法及线路实现

随着小波理论研究的深入,以及小波分析在信号分析和图像处理等领域的广泛应用,小波分析在量子计算领域中也越来越受到重视.应用置换矩阵、W-H变换矩阵和量子傅立叶变换矩阵来对Haar小波及D(4)小波变换矩阵进行分解,给出其算法,然后得出其完整的量子逻辑线路图,最后分析其复杂度.     

小波变换在医学图像处理上的应用

小波变换是对傅立叶变换的继承和发展,近年来发展迅速,已广泛应用于图像处理、生物医学信号提取、语音合成、地震信号处理等众多领域.小波变换特别适用于提取微弱、背景噪声较强的随机信号,处理医学图像信号这一类非平稳信源.简要介绍了小波变换的原理和特点,综述了小波变换在医学图像压缩、去噪、增强、边缘提取、图像融合等方面的应用.     

Fractional dual tree complex wavelet transform and its application to biometric security during communication and transmission

In this paper, the dual tree complex wavelet transform, which is an important tool and recent advancement in signal and image processing, has been generalized by coalescing dual tree complex wavelet transform and fractional Fourier transform. The new transform, i.e. the fractional dual tree complex wavelet transform (FrDT-CWT) inherits the excellent mathematical properties of dual tree complex wavelet transform and fractional Fourier transform. Possible applications of the proposed transform are in biometrics, image compression, image transmission, transient signal processing etc. In this paper, biometric is chosen as the primary application and hence a new technique is proposed for securing biometrics during communication and transmission over insecure channel.     

An adaptive edge-preserving image denoising technique using patch-based weighted-SVD filtering in wavelet domain

Image denoising has always been one of the standard problems in image processing and computer vision. It is always recommendable for a denoising method to preserve important image features, such as edges, corners, etc., during its execution. Image denoising methods based on wavelet transforms have been shown their excellence in providing an efficient edge-preserving image denoising, because they provide a suitable basis for separating noisy signal from the image signal. This paper presents a novel edge-preserving image denoising technique based on wavelet transforms. The wavelet domain representation of the noisy image is obtained through its multi-level decomposition into wavelet coefficients by applying a discrete wavelet transform. A patch-based weighted-SVD filtering technique is used to effectively reduce noise while preserving important features of the original image. Experimental results, compared to other approaches, demonstrate that the proposed method achieves very impressive gain in denoising performance.     

电动机故障诊断技术探讨

介绍了电动机常见电气故障和机械故障的类型及产生原因,详细阐述了短时傅里叶变换、小波变换、小波包变换、经验模态分解等基于信号处理的诊断方法,以及基于专家系统、模糊理论、支持向量机、神经网络等的智能诊断方法在电动机故障诊断中的应用,指出多种诊断方法相结合以及信息融合方法是电动机故障诊断技术的发展趋势。